第三章建立了基于非线性区间函数风险控制的资产负债组合优化模型。
The second chapter structures the optimal model of asset portfolio to control both credit and interest rate risks.
证明过程中主要应用了分析中的压缩映象原理和一些空间的性质，通过构造可计算函数，来把解从一个区间延拓到整个空间。
We mainly apply the contraction principle in analysis and properties of some Spaces. By the computable functions constructed, we extend the solution from the internal to the entire space.
此外，通过允许选择函数在一个区间中取值，推广了随机选择的概念。
Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized.
良有界算子是这样一类算子，它对于在某个紧区间上绝对连续的函数具有有界的函数演算。
Well-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact intervals.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
提出了一种新的带权的区间值模糊产生式规则，给出了加权模糊匹配函数和一个区间值排序算法。
In this paper, we propose a new interval-valued fuzzy production rule with weight, and provide weighted fuzzy matching function and an algorithm of interval value ranking.
同时，拟合方法采用目前非常成熟的多项式最小二乘拟合。从而不仅能控制拟合函数的复杂性，而且使分段拟合的补偿区间数量达到最少，极大地降低了计算成本。
The paper adopts the method of multinomial least squares as fitting to make the fitting function be simple and the amount of compensation interval be least, reduces the calculation cost.
最后还证明了对于实数的子集a，如果定义在A上取值于A内的任一连续函数都有不动点，则A为实数的有限闭区间。
And finally we prove that let a be a subset of real Numbers, if every continuous function which is defined on a and taken value in a has fixed point, then a is a finite closed interval.
本文就二次可微函数类给出一类求大范围极值的区间迭代方法。
In this paper an interval iterative method is given for seeking the global maximum of a second order differentiable function.
给出了填充函数的区间扩张，并提出了求解该非光滑优化问题的区间填充函数算法。
It gives an interval enclosure for filled function and presents an interval filled function algorithm to solve this nonsmooth optimization.
康托尔定理出发，清晰的给出在任意区间的函数一致连续的条件，并且讨论非一致连续的简单的判别方法。
Cantor, the paper presents conditions of uniform continuity of a function in arbitrary boundary, and discusses the simple distinguish method for nonuniform continuity.
阐述了爆破地震波的质点最大振速V是一个随机变量，它与Q、R没有一般意义上确定的函数关系，因此振动只能控制在某一区间。
The maximum velocity V in blasting vibration is a random variable, it has no definite function relation to Q and R in general meaning. So V only can be controlled in a confidence interval.
该区间估计中包含了目标函数的一个最优估计值。
This estimated interval contained an estimated value of goal function.
通过加权函数，即着眼于与中间部分而不是区间端点附近，这样就完成了加窗。
This windowing is accomplished via a weight function that places less emphasis near the interval's endpoints than in the middle.
应用闭区间连续函数性质和实数连续性定理，给出证明广义中值定理的一个新思路。
Closed interval continuous function and continuity theorem of real number apply to a novel demonstration of general theorem of the mean.
定义了区间I上的均匀可导函数，给出了区间i上函数均匀可导的两个充要条件。
The uniformly derivable function on the interval I is defined, and two sufficient and necessary conditions of uniformly derivable function are given.
给出了一种不含导数的函数展开方法，在函数的连续区间内构造一个无穷级数作为函数的展开式。
To construct a progression at infinity as an expansion of function in the continuous interval, a good result was achieved.
用数学分析中的区间套定理证明了闭区间上连续函数的四个定理。
Four theorems about continuous function on an closed interval are proved by a interval sequence theorem in mathematical analysis.
研究发现，当蚌密度在每立方米6.25个到每立方米31.25个的区间内，时效模型呈具有极大值的抛物线函数。
Statistics showed that the time-effect models are parabola functions with maximum values when the mussel population density ranges from 6.25 to 31.25 per cubic meter.
定义了区间值函数的RS积分，并利用它来定义模糊值函数的RS积分，给出了这种积分的一些性质。
RS integral of interval valued functions and Fuzzy valued functions are defined. Some properties of this kind of integral are obtained.
并对约束系数和目标函数系数为区间数的线性规划问题进行了深入的分析。
The linear programming with interval number in target function and constraint coefficient is analyzed thoroughly.
函数在其定义区间内都是连续的。
Every elementary function is continuous on its well-defined intervals.
讨论了一类多目标优化问题的区间斜率方法，其中目标函数是一阶连续可微的。
This paper describes the interval slope methods for a class of multiobjective optimization problems, of which the objective functions are in C1.
先将不等式转化成函数不等式，然后在每个局部区间上证明不等式。
Namely, the inequality should be transformed into function inequality first and then the inequality can be proved by an interval of each segment.
分别对区间目标函数、区间不等式约束和区间等式约束作了讨论。
Interval objective function, interval inequality constraints and interval equality constraints were discussed separately.
目前，我国大多学者在运用效用函数确定保险费率时，都以投保人全额投保和保险人全额赔付为前提推出保险费率的定价区间。
Nowadays, all articles which apply the utility theory to determine the premium rates give priority to the fully insured and full payment in order to get the price range of premium rate.
给出了一元函数在区间上一致连续的一个等价条件，并运用它证明了一些函数的一致连续性。
AN equivalent condition of function's consistent continuity is proved. Application of it in several examples is showed.
阐述了利用导数知识研究函数的单调区间、大值最小值等问题的基本方法，以及导数方法为解决某些不等式的证明、列求和等问题提供了捷径。
It explains some basic ways of how to use derivative to study monotonous zone in function, to calculate maximum and minimum, and how to solve some problems on inequality and number sequence, etc.
阐述了利用导数知识研究函数的单调区间、大值最小值等问题的基本方法，以及导数方法为解决某些不等式的证明、列求和等问题提供了捷径。
It explains some basic ways of how to use derivative to study monotonous zone in function, to calculate maximum and minimum, and how to solve some problems on inequality and number sequence, etc.
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